Cumulative Residual Extropy for Pareto Distribution in the Presence of Outliers: Bayesian and Non-Bayesian Methods

Amal Hassan; Elsayed Elsherpieny; Rokaya Mohamed

doi:10.19139/soic-2310-5070-1200

Amal Hassan Faculty of Graduate Studies for Statistical Research, Cairo University, Egypt https://orcid.org/0000-0003-4442-8458
Elsayed Elsherpieny Faculty of Graduate Studies for Statistical Research, Cairo University, Egypt
Rokaya Mohamed Faculty of Graduate Studies for Statistical Research, Department of Mathematical Statistics, Cairo University

DOI: https://doi.org/10.19139/soic-2310-5070-1200

Keywords: Pareto distribution, outliers, extropy, cumulative residual extropy, Metropolis-Hastings algorithm

Abstract

The extropy is considered to be a complementary dual of the well-known Shannon’s entropy and has wide applications in many fields. This article discusses estimating the extropy and cumulative residual extropy of the Pareto distribution using the maximum likelihood and Bayesian methods. We obtain the maximum likelihood of extropies measures in presence of outliers. These estimators are specialized to homogenous case. The Bayesian estimators of both extropy measures are derived based on symmetric and asymmetric loss functions. The Markov chain Monte Carlo methods are used to accomplish some complex calculations. The precision of the Bayesian and the maximum likelihood estimates for extropy estimates are examined through simulations. Regarding results of simulation study, we conclude that the performances of both estimation methods improve with sample sizes. Also, Bayesian estimates of the extropy and cumulative residual extropy under linear exponential loss function are superior to the other Bayesian estimates under the other loss functions in most of cases. The performance for the extropy and cumulative residual extropy estimates increase with number of outliers in almost cases. Generally, there is a great agreement between the theoretical and empirical results. Further performance comparison is conducted by the experiments with real data.

Author Biographies

Amal Hassan, Faculty of Graduate Studies for Statistical Research, Cairo University, Egypt

Professor of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research: Giza, Egypt

Elsayed Elsherpieny, Faculty of Graduate Studies for Statistical Research, Cairo University, Egypt

Professor of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research: Giza, Egypt

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